In this talk, we study the observability for the Schrödinger equation on the two-dimensional torus, subject to a first-order perturbation by a magnetic potential. This situation turns out to be different from the case of the Schrödinger equation with a purely electric potential. More precisely, there is a sufficient and almost necessary geometric control condition for the electromagnetic Schrödinger equation that goes beyond the classical geometric control condition established by Lebeau for the unperturbed case. We prove the observability under this new geometric condition.  This talk is based on joint work with Kévin Le Balc'h and Chenmin Sun.